SOLUTION The logistic growth function f(t) 50, 000

SOLUTION: The logistic growth function f(t) =50,000/1 + 1249.0e-1.3t models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a part. You can put this solution on YOUR website! if you don't insert parentheses where they belong then you run into trouble. you equation needs to be: f(t) = 50000/(1+1249*e^(-1.3t)) note the parentheses around the exponent. this insures the entire expression of -1.3t is treated as part of the exponent of e. note the parentheses around (1+1249*e^(-1.3t)) this insures the entire expression of (1+1249*e^(-1.3t)) is included in the denominator. you can graph this equation by replacing f(t) with y and replacing t with x. then you can see what the equation looks like. you have to be a little creative with the dimensions of the graph. after some fiddling, i settled on the range of the x-axis being -15 to 25, and the range of the y-axis being -1000 to 100,000. this allowed me to see what was going on. what was going on is that the equation starts off small and then rises to about 50000 and then flattens out and doesn't go any higher than 50,000. replacing x with some selected values and calculating y for those values yields a table similar to what you see below: by the time x gets to 15, it has saturated to y = 50,000 which is the limiting value of the function. the above values have been rounded to the nearest integer. this is caused by the denominator of (1 + 1249 * e^(-1.3*x) becoming very close to 1 as x gets larger than 15; close enough that the numerator of 50,000 is effectively being divided by 1. for example, (1 + 1249*e^(-1.3*x) is equal to (1 + .0000042444. ) which becomes 1.0000042444 which is pretty darn close to 1. 50000 divided by 1.0000042444 is equal to 49999.787778 that is very close to 50,000 and gets even closer as x gets larger than 15. when x = 20, the function becomes y = 49999.99968. that even closer. when you round the result to the nearest integer, you get 50,000 for both x = 15 and x = 20. don't forget to use parentheses to ensure the function is being displayed correctly. take some spot measurements if you don't have a graphing calculator so you can see what is happening. the limiting value of your function is 50,000.